Probability and Statistics - Exam Questions with Verified Answers Latest Update 2025 Graded A+
Alpha - Answers committing a Type I error
Alternate Hypothesis - Answers Denoted by H(a), is the assertion that is contradictory to H(not).
Analysis of variance - Answers refers broadly to a collection of experimental situations and statistical
procedures for the analysis of quantitative responses from experimental units. Tests the difference
between group means after any other variance in the outcome variable is accounted for
Beta - Answers a Type II error
Between-group variance - Answers Differences between group means.
Chi-Square distribution - Answers With k degrees of freedom, is the distribution of a sum of the squares
of k independent standard normal random variables. Tests for the strength of the association between
two categorical variables
Coefficient of determination - Answers (Denoted by R2) is a key output of regression analysis. It is
interpreted as the proportion of the variance in the dependent variable that is predictable from the
independent variable.
Confidence Interval - Answers A range of values so defined that there is a specified probability that the
value of a parameter lies within it. Always calculated by first selecting a confidence level.
Confidence level - Answers The probability that the value of a parameter falls within a specified range of
values. Is a measure of the degree of reliability of the interval.
Contingency table - Answers A table showing the distribution of one variable in rows and another in
columns, used to study the association between the two variables.
Correlation - Answers association between variables. relationship between z variables, call them x and y
Correlation Coefficient - Answers A number R between −1 and +1 calculated so as to represent the linear
dependence of two variables or sets of data. When applied to a sample is commonly represented by the
letter r. measures the strength and direction of a linear relationship between the z - variables. sample
Critical or rejection region - Answers The set of all test statistic values for which H(not) will be rejected.
The set of values for the test statistic that leads to the rejection of the null hypothesis.
Critical value - Answers A point on the test distribution that is compared to the test statistic to
determine whether to reject the null hypothesis. Are values that separate the rejection and nonrejection
region. Is part of the rejection region.
Degrees of Freedom - Answers Is the number of values in the final calculation of a statistic that are free
to vary.
, Dependent variable - Answers For fixed x, the second variable will be random; we denote this random
variable and its observed value by Y and y, respectively, and refer to it as the response variable.
Explanatory variable - Answers Is a type of independent variable. When a variable is independent, it is
not affected at all by any other variables. Also, when a variable isn't independent for certain. The
variable whose value is fixed by the experimenter will be denoted by x and will be called the
independent or predictor. Explained by the relationship between x and y
Factors - Answers The characteristic that differentiates the treatments or populations from one another.
Goodness-of-fit test - Answers The extent to which observed data match the values expected by theory.
Homogeneity of proportions test - Answers Is a method, based on the chi-square statistic, for testing
whether two or more multinomial distributions are equal.
Hypothesis Testing - Answers A method for using sample data to decide whether the null hypothesis
should be rejected.
Independence test - Answers The relationship between two different factors in a single population. Each
individual in the population is assumed to belong in exactly one of the I categories associated with the
first factor and exactly one of the J categories associated with the second factor. The claim is that the
row and column variables are independent of each other. This is the null hypothesis. Tests for difference
between two independent variables
Independent variable - Answers
Interval estimate - Answers An alternative to reporting a single sensible value for the parameter being
estimated is to calculate and report an entire interval of plausible values. An interval within which the
value of a parameter of a population has a stated probability of occurring.
Least-square line - Answers Is the one that has the smallest possible value for the sum of the squares of
the residuals.
Level - Answers The different treatments or populations. Number of treatment conditions (groups).
Level of significance - Answers A Type I error occurs when the researcher rejects a null hypothesis when
it is true. The probability of committing a Type I error, it is often denoted by α. The null hypothesis is
rejected if the p-value is less than a predetermined level, α. It is the probability of rejecting the null
hypothesis given that it is true (a type I error). It is usually set at or below 5%.
Maximum error of estimate - Answers Denoted by E and is one-half the width of the confidence interval.
Mean Square - Answers (In an ANOVA), refers to an estimate of the population variance based on the
variability among a given set of measures.
Multiple correlation coefficient - Answers The positive square root of R2. Measure of how well a given
variable can be predicted using a linear function of a set of other variables. It is the correlation between
Alpha - Answers committing a Type I error
Alternate Hypothesis - Answers Denoted by H(a), is the assertion that is contradictory to H(not).
Analysis of variance - Answers refers broadly to a collection of experimental situations and statistical
procedures for the analysis of quantitative responses from experimental units. Tests the difference
between group means after any other variance in the outcome variable is accounted for
Beta - Answers a Type II error
Between-group variance - Answers Differences between group means.
Chi-Square distribution - Answers With k degrees of freedom, is the distribution of a sum of the squares
of k independent standard normal random variables. Tests for the strength of the association between
two categorical variables
Coefficient of determination - Answers (Denoted by R2) is a key output of regression analysis. It is
interpreted as the proportion of the variance in the dependent variable that is predictable from the
independent variable.
Confidence Interval - Answers A range of values so defined that there is a specified probability that the
value of a parameter lies within it. Always calculated by first selecting a confidence level.
Confidence level - Answers The probability that the value of a parameter falls within a specified range of
values. Is a measure of the degree of reliability of the interval.
Contingency table - Answers A table showing the distribution of one variable in rows and another in
columns, used to study the association between the two variables.
Correlation - Answers association between variables. relationship between z variables, call them x and y
Correlation Coefficient - Answers A number R between −1 and +1 calculated so as to represent the linear
dependence of two variables or sets of data. When applied to a sample is commonly represented by the
letter r. measures the strength and direction of a linear relationship between the z - variables. sample
Critical or rejection region - Answers The set of all test statistic values for which H(not) will be rejected.
The set of values for the test statistic that leads to the rejection of the null hypothesis.
Critical value - Answers A point on the test distribution that is compared to the test statistic to
determine whether to reject the null hypothesis. Are values that separate the rejection and nonrejection
region. Is part of the rejection region.
Degrees of Freedom - Answers Is the number of values in the final calculation of a statistic that are free
to vary.
, Dependent variable - Answers For fixed x, the second variable will be random; we denote this random
variable and its observed value by Y and y, respectively, and refer to it as the response variable.
Explanatory variable - Answers Is a type of independent variable. When a variable is independent, it is
not affected at all by any other variables. Also, when a variable isn't independent for certain. The
variable whose value is fixed by the experimenter will be denoted by x and will be called the
independent or predictor. Explained by the relationship between x and y
Factors - Answers The characteristic that differentiates the treatments or populations from one another.
Goodness-of-fit test - Answers The extent to which observed data match the values expected by theory.
Homogeneity of proportions test - Answers Is a method, based on the chi-square statistic, for testing
whether two or more multinomial distributions are equal.
Hypothesis Testing - Answers A method for using sample data to decide whether the null hypothesis
should be rejected.
Independence test - Answers The relationship between two different factors in a single population. Each
individual in the population is assumed to belong in exactly one of the I categories associated with the
first factor and exactly one of the J categories associated with the second factor. The claim is that the
row and column variables are independent of each other. This is the null hypothesis. Tests for difference
between two independent variables
Independent variable - Answers
Interval estimate - Answers An alternative to reporting a single sensible value for the parameter being
estimated is to calculate and report an entire interval of plausible values. An interval within which the
value of a parameter of a population has a stated probability of occurring.
Least-square line - Answers Is the one that has the smallest possible value for the sum of the squares of
the residuals.
Level - Answers The different treatments or populations. Number of treatment conditions (groups).
Level of significance - Answers A Type I error occurs when the researcher rejects a null hypothesis when
it is true. The probability of committing a Type I error, it is often denoted by α. The null hypothesis is
rejected if the p-value is less than a predetermined level, α. It is the probability of rejecting the null
hypothesis given that it is true (a type I error). It is usually set at or below 5%.
Maximum error of estimate - Answers Denoted by E and is one-half the width of the confidence interval.
Mean Square - Answers (In an ANOVA), refers to an estimate of the population variance based on the
variability among a given set of measures.
Multiple correlation coefficient - Answers The positive square root of R2. Measure of how well a given
variable can be predicted using a linear function of a set of other variables. It is the correlation between
